MinT - Best Known (82−32, 82, s)-Nets in Base 32

Best Known (82−32, 82, s)-Nets in Base 32

(82−32, 82, 300)-Net over F₃₂ — Constructive and digital

Digital (50, 82, 300)-net over F₃₂, using

1 times m-reduction [i] based on digital (50, 83, 300)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]
  2. digital (7, 23, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (9, 42, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(82−32, 82, 516)-Net in Base 32 — Constructive

(50, 82, 516)-net in base 32, using

1 times m-reduction [i] based on (50, 83, 516)-net in base 32, using
- (u,Â u+v)-construction [i] based on
  1. (12, 28, 258)-net in base 32, using
    - base change [i] based on (4, 20, 258)-net in base 128, using
      - 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
        base change [i] based on digital (1, 21, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. (22, 55, 258)-net in base 32, using
    - 1 times m-reduction [i] based on (22, 56, 258)-net in base 32, using
      - base change [i] based on digital (1, 35, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(82−32, 82, 3853)-Net over F₃₂ — Digital

Digital (50, 82, 3853)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−32, 82, large)-Net in Base 32 — Upper bound on s

There is no (50, 82, large)-net in base 32, because

30 times m-reduction [i] would yield (50, 52, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]